Adding a 'distortion effect' to a model
I'll demonstrate you some mesh deformation methods using poor Suzanne ;). 




USING PROPORTIONAL EDITING WITH RANDOM FALLOFF TYPE




The simplest way you can do I think is to go to Edit Mode and click Select-->Random, while vertex selection mode is enabled. 
Now you can enable the proportional editing with Random falloff type, then grab, rotate and scale some vertices to make deformations.


Remember, that you can set deformed vertices' transformations as a shape key to not destruct your base mesh.





USING LATTICE MODIFIER




Being in Object Mode add a Lattice (Add-->Lattice). Subdivide it using options in Object Data header, and place your object inside it. Give your object a Lattice Modifier and set everything as pictured below. Select your Lattice, enter Edit Mode, select some random Lattice vertices, then grab, rotate and scale them (also using Random falloff of the proportional editing).





USING MESH DEFORM MODIFIER (for a better control over deformations)




Create a low poly representation of your object and name it for example 'cage'. Place your object inside it. Give it a Mesh Deform Modifier and set everything as pictured below. Give the Precision factor a low value (the bigger the value, the more possibility, that your computer'll cry ;)). Next click the Bind button to bind your object to a low poly 'cage' mesh. Now, when you deform vertices of the 'cage' your object's vertices will be deformed as well.


Try to mix these for better result.